If 2/3 of a number is 432, what is 3/4 of that number?
Understand the Problem
The question is asking us to find out what three-fourths of a number is, given that two-thirds of that number equals 432. To solve this, we first need to determine the full number by using the relationship between fractions and then calculate three-fourths of that result.
Answer
$486$
Answer for screen readers
The final answer is $486$.
Steps to Solve
- Define the variable
Let the unknown number be denoted as $x$.
- Set up the equation
From the problem, we know that two-thirds of the number equals 432. This can be represented as: $$ \frac{2}{3}x = 432 $$
- Solve for $x$
To find $x$, we first multiply both sides of the equation by 3 to eliminate the denominator: $$ 2x = 432 \times 3 $$ Thus, $$ 2x = 1296 $$
Next, we divide both sides by 2: $$ x = \frac{1296}{2} $$ So, $$ x = 648 $$
- Calculate three-fourths of $x$
Now, we need to find three-fourths of the number $x = 648$. This can be calculated as: $$ \frac{3}{4} \times 648 $$
- Multiply to find the final answer
Calculating this gives us: $$ \frac{3 \times 648}{4} = \frac{1944}{4} = 486 $$
The final answer is $486$.
More Information
The problem requires you to understand fractions and how to manipulate equations to isolate variables. It showcases how to work with proportions of numbers, which is a common mathematical concept.
Tips
- One common mistake is forgetting to correctly multiply or divide both sides of the equation. Always perform the same operation on both sides of the equation to maintain equality.
- Another mistake could be miscalculating the final multiplication or division steps. Double-checking calculations can help prevent errors.
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